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7. Write an algebraic expression that represents the following:

Three less than the sum of nine and a number cubed.

What is the value when [tex]n = 2[/tex]?

Expression:

Value: (Show your work)

Sagot :

GinnyAnsweridn
Sure, let's break this problem down step by step.

### Step 1: Write the Algebraic Expression

The problem states:
"Three less than the sum of nine and a number cubed."

Let's denote the unknown number as [tex]\( n \)[/tex].

1. First, calculate the number cubed: [tex]\( n^3 \)[/tex].
2. Next, find the sum of nine and this cubed value: [tex]\( 9 + n^3 \)[/tex].
3. Finally, subtract three from this sum: [tex]\( (9 + n^3) - 3 \)[/tex].

So, the algebraic expression is:
[tex]\[ (9 + n^3) - 3 \][/tex]

Let's simplify this expression. The simplified version is:
[tex]\[ n^3 + 6 \][/tex]

### Expression
[tex]\[ n^3 + 6 \][/tex]

### Step 2: Determine the Value When [tex]\( n = 2 \)[/tex]

Now, we substitute [tex]\( n = 2 \)[/tex] into the expression [tex]\( n^3 + 6 \)[/tex].

1. Calculate [tex]\( 2^3 \)[/tex]:
[tex]\[ 2^3 = 8 \][/tex]

2. Plug [tex]\( 2^3 \)[/tex] into the simplified expression:
[tex]\[ 8 + 6 \][/tex]

3. Perform the addition:
[tex]\[ 8 + 6 = 14 \][/tex]

### Value
[tex]\[ 14 \][/tex]

So, the algebraic expression representing "three less than the sum of nine and a number cubed" is [tex]\( n^3 + 6 \)[/tex]. When [tex]\( n = 2 \)[/tex], the value of this expression is 14.
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